Positivity and Stability Analysis of Homogeneous Coupled Differential-Difference Equations With Time-Varying Delays
Yukang Cui, Jun Shen, Wei Zhang, Zhiguang Feng, Xin Gong
Abstract
This article studies the positivity and stability of homogeneous coupled differential-difference equations with time-varying delays. First, a sufficient positivity condition is proposed for the nonlinear coupled differential-difference equations with delays. Then, based on this positivity condition, we present necessary and sufficient conditions ensuring the exponential stability and bounding the decay rate for time-delay homogeneous coupled differential-difference equations with homogeneity of degree one. Furthermore, the necessary and sufficient condition is extended to the global polynomial stability analysis of homogeneous coupled differential-difference equations when the degree of homogeneity is greater than one, and the decay rate is also investigated. Two numerical examples are employed to show the effectiveness of the obtained results.